Nonlinear Frequency Mixing of Counter-Propagating Lamb Waves at a Contacting Interface of Plates

Abstract The nonlinear interaction of two counter-propagating Lamb waves with a contacting interface of plates, which generates their mixed-frequency components, is investigated as a basis of closed-defect characterization. In this article, a one-dimensional analysis of the frequency mixing at a nonlinear spring-type interface is first laid down to illustrate its basic features. The frequency mixing measurements using the lowest-order symmetric Lamb waves are then described for two types of contacting interfaces, i.e., plate−plate contacting edges and a fatigue crack. A theoretical model of the measurement process is formulated to establish the strategy for spatially scanning the mixing zone of Lamb waves. As a result, the generation of the sum-frequency component is demonstrated experimentally when the mixing zone is scanned across the interface, with its power attaining the maximum at the interface and its arrival time being consistent with the theoretical estimate. It is also shown that the sum-frequency component propagates in both directions from the interface, and its amplitude is proportional to the product of the primary-wave amplitudes. These results indicate that it is possible not only to detect a closed defect in a plate but also to identify its location by the mixing zone scanning of Lamb waves.